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Algebras of iterated path integrals and fundamental groups. (English) Zbl 0217.47705


MSC:

53C65 Integral geometry
58A99 General theory of differentiable manifolds
Full Text: DOI

References:

[1] Kuo-Tsai Chen, Iterated integrals and exponential homomorphisms, Proc. London Math. Soc. (3) 4 (1954), 502 – 512. · Zbl 0058.25603 · doi:10.1112/plms/s3-4.1.502
[2] Kuo-Tsai Chen, Integration of paths, geometric invariants and a generalized Baker-Hausdorff formula, Ann. of Math. (2) 65 (1957), 163 – 178. · Zbl 0077.25301 · doi:10.2307/1969671
[3] Kuo-Tsai Chen, Integration of paths — a faithful representation of paths by non-commutative formal power series, Trans. Amer. Math. Soc. 89 (1958), 395 – 407. · Zbl 0097.25803
[4] Kuo-Tsai Chen, Exponential isomorphism for vector spaces and its connection with Lie groups, J. London Math. Soc. 33 (1958), 170 – 177. · Zbl 0083.02202 · doi:10.1112/jlms/s1-33.2.170
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[9] Kuo-tsai Chen, An algebraic dualization of fundamental groups, Bull. Amer. Math. Soc. 75 (1969), 1020 – 1024. · Zbl 0182.57101
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[16] A. N. Paršin, On a certain generalization of Jacobian manifold, Izv. Akad. Nauk SSSR Ser. Mat. 30 (1966), 175 – 182 (Russian).
[17] Rimhak Ree, Lie elements and an algebra associated with shuffles, Ann. of Math. (2) 68 (1958), 210 – 220. · Zbl 0083.25401 · doi:10.2307/1970243
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[19] André Weil, Introduction à l’étude des variétés kählériennes, Publications de l’Institut de Mathématique de l’Université de Nancago, VI. Actualités Sci. Ind. no. 1267, Hermann, Paris, 1958 (French). · Zbl 0137.41103
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